Hi Ciro,
So you are using a marble saddle?
Definitely caulk the joint between the tiles and the saddle like you are planning. Then caulk the joint between the saddle and the hardwood floor. You can use tape over the hardwood floor while caulking to assist in keeping the caulk very neat. If the hardwood is perpendicular, rather than parallel to the saddle, you might be able to get away with bringing the saddle up to the hardwood with no caulk.....
but that crack is going to catch dirt and look crappy after awhile. I'd stick to caulking both sides of that saddle.